Scrub the quinces with a damp towel to remove all the fuzz from the skin. Cut them into quarters and remove the core and any hard pith, then cut each quarter lengthwise in half. Leave on the skin; it contains flavor and pectin.
Bring about 4 cups (1 liter) water to a boil in the bottom half of a steamer. Place the quinces in the top half, cover, and steam until they are soft through, about 25 minutes.
Transfer the quinces to a food processor and puree. Strain the puree through a fine sieve so it is completely smooth, and transfer it to a large, heavy-bottomed saucepan. Add 4 ups (800g) of the sugar and stir until thoroughly combined, then add the lemon zest. Bring to a boil over medium heat, reduce the heat to medium-low, and cook, stirring, until the mixture becomes very thick and gelatinous, and turns the color of light terra cotta, which will take 30 to 35 minutes.
Sprinkle 2 tablespoons sugar evenly over a 13.16 inch (32.5 x 40cm) surface or non-reactive baking sheet.
When the quince paste is cooked, turn it onto the prepared surface and smooth it out as quickly as you can until it is approximately 1/4-inch (0.6cm) thick. Sprinkle it evenly with the remaining 2 tablespoons sugar and leave it to cool completely.
When the paste has cooled, cut it into 2-inch (5cm) diamond shapes. Store in an airtight container layered with parchment paper, in a cool place (not the refrigerator).